Abstract
Abstract We consider the recursive estimation of the unknown parameters in the stochastic differential equation describing the system utilizing the observations of the state of the system. We show that the unknown parameters can be divided into two groups so that the true values of the members of the first group can be recovered instantaneously whereas the true values of the members of the second group cannot be recovered in finite time. We derive the recursive equations for the conditional mean and covariance of the unknown parameters of the second. Then we consider the determination of the optimal feedback control function for minimizing a suitable criterion function. We will show that the optimal feedback control is a function of the current state measurement, the conditional mean and variance of the unknown parameters. We mention a method of approximation of the optimal feedback control function and the results of the simulation of the control scheme.
Published Version
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